CORRECTION OF THEOCTUPOLE TERM
INTRODUCED BY THEWIGGLER MAGNET
Claudio SanelliMiro Andrea Preger
Preliminary considerations• Measurements with beam on the wiggler have shown the
presence of an octupole-like term coming from thecombination of a decapole term in the wiggler field with thewiggling trajectory of the beam
• The tune shift as a function of beam position in the wigglerhas been fitted in the machine model with a single octupolarthin lens at the wiggler center and with 5 thin lenses, one ineach pole
• The intensity of the octupole lens, according to the differentmodels, in MAD units is
• 500 m-3 < KMAD < 1000 m-3
First attempt:Wiggler end plate modification
Wiggler 3D simulation
Longitudinal field profile(3D simulation)
Longitudinal field profile comparisonwith and without end plate
Naive approach to endplate profile shaping
• Assume field inversely proportional to endplate gap g:• (Bc + hx3)*g = const = Bc*g• Assume endplate contribution to the field from magnetic
calculations Bc 0.18 T• Add linear term in the field to avoid excessive reduction of
the gap:• (Bc + kx + hx3 )*g = const = Bc*g• Truncate gap oscillation to constant to avoid excessive
reduction of the gap• Run magnetic calculation to find the real field
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08
halfgap (m) = 0.0036/B(x)B(x) = 0.18 + 4700*(x+0.0125)^3 - 3.2*(x+0.0125)
G=0B=3.2*x
x(m)
halfgap (m)
End plate 2D simulation
Transverse field profile under theend plate – no shaping
End plate shaping(2 D simulation)
Transverse field profile under theend plate
Field profile modification
0.125
0.130
0.135
0.140
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03
KMAD
(per endplate) 50 m-3
B(T)
x(m)
Y = M0 + M1*x + ... M8*x 8 + M9*x9
0.13171M0
-0.26269M1
0.095223M2
431.42M3
0.95406R
0.125
0.130
0.135
0.140
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03
KMAD
(per endplate) 135 m-3
B(T)
x(m)
Y = M0 + M1*x + ... M8*x 8 + M9*x9
0.13141M0
-0.57437M1
1.8053M2
1259.3M3
-1160.9M4
-4.2274e+05M5
0.99854R
1st Attempt: Conclusions
• Bad magnetic field profile
• Insufficient octupole term correction
DISCARDED
Second attempt:Substitution of the end plate with
PM blocks
Longitudinal field profile(3 D simulation)
Longitudinal field profile comparisonwith and without end plate
PM Block geometry(2 D simulation)
Transverse magnetic field profile
Magnetic field near the beam axis
PM Blocks – 3 D geometry
PM Blocks – 3 D solution area
PM Blocks – 3 D solution
Transverse magnetic field profile
Longitudinal magnetic field profile
2 D – 3 D comparisonTransverse field profile
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
-0.05 0.00 0.05
2-D KMAD
230 m-3 (per endplate)
B (T)
x (m)
Y = M0 + M1*x + ... M8*x 8 + M9*x9
2.0254e-07M0
-0.12356M1
-0.00010666M2
2343.8M3
1R
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
-0.05 0.00 0.05
3-D KMAD
120 m-3 (per endplate)
B (T)
x (m)
Y = M0 + M1*x + ... M8*x 8 + M9*x9
-7.9512e-18M0
0.52448M1
1.0372e-14M2
1239.5M3
0.9985R
2nd Attempt: Conclusions
• Acceptable field quality but very critical withrespect to magnet position and size
• Insufficient octupole term correction
DISCARDED
Third attempt:
Octupole correction added intoANSALDO Large Sextupole
by means of awired, air cooled, coil
•
•
Sextupole 2D simulation
L.S. Symmetric Sextupole FieldProfile
Sextupole + Octupole
Sextupole + OctupoleIcorr = 600 A-turns
Sextupole + Octupole correctionBz(x, Icorr)
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Sextupole @ 175A, Octupole @ 600A
KMAD
60 m-3
x (m)
Y = M0 + M1*x + ... M8*x 8 + M9*x9
-0.0013124M0
-0.42625M1
-97.241M2
-111M3
0.9999R
B (T)
3rd Attempt: Conclusions
• Reasonably good magnetic field profile
• Insufficient octupole term correction
DISCARDED
Fourth attempt:
Octupole correction added intoANSALDO Large Sextupole
by means of awater cooled, coil
W.C. coil front view
Sextupole + Octupole2D simulation
Sextupole + OctupoleIcorr=3296A*t – Field profile
Sextupole used as OctupoleIcorr = 3296 A*t
Sextupole as OctupoleMagnetic field profile
Sextupole as OctupoleMagnetic field profile
Sextupole as OctupoleKMAD ≈ 330 m-3
Sextupole as OctupoleNo quadrupole
Coil data (1st option)• Coil cross section mm*mm 50 * 14
• Conductor: Cu mm*mm 5.6*5.6
• Cooling hole dia. mm 3.6
• Turns per coil 16
• Coils per Sextupole 4
• Maximum current A 206
• Current density A/mm2 10.14
• Magnet voltage V 17.32
• Magnet power W 3568
• Hydr. Circ. per magnet 4
• Water velocity m/s 1.05
• Water flow per magnet m3/s 4.3E-5
• Temperature increase °C 20
• Pressure drop MPa 0.143
Coil data (2nd option)• Coil cross section mm*mm 44 * 14
• Conductor: Cu mm*mm 5.6*5.6
• Cooling hole dia. mm 3.6
• Turns per coil 14
• Coils per Sextupole 4
• Maximum current A 235.4
• Current density A/mm2 11.58
• Magnet voltage V 18.21
• Magnet power W 4288
• Hydr. Circ. per magnet 4
• Water velocity m/s 1.26
• Water flow per magnet m3/s 5.2E-5
• Temperature increase °C 20
• Pressure drop MPa 0.18
However, before going ahead:
• Systematic check of the available spacebetween vacuum chamber-sextupole
• Mechanical coil design (electric terminals,hydraulic spigots, coil supports, etc.)
• Mechanical 3D check to verify coil insertionwithout sextant splitting
• Preliminary industry check
4th Attempt: Conclusions
• Good magnetic field profile
• Quadrupole gradient of about 2.3 T/m to be corrected
• Reasonably good technical solution
POSSIBLE SOLUTION